- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Polymerized spacetime dynamics with multifield source: Unraveling the preinflationary Universe

Divya Gupta1,*, Manabendra Sharma1,†, Gustavo S. Vicente2,‡, Rudnei O. Ramos3,§, and Anzhong Wang4,∥

  • *Contact author: divya920818@gmail.com
  • †Contact author: sharma.man@mahidol.ac.th
  • ‡Contact author: gustavo@fat.uerj.br
  • §Contact author: rudnei@uerj.br
  • ∥Contact author: Anzhong_Wang@baylor.edu
PDF

Phys. Rev. D 114, 043503 – Published 4 August, 2026

DOI: https://doi.org/10.1103/6f4f-76ty

Abstract

We study a multifield model in loop quantum cosmology for a maximally symmetric spacetime governed by the Einstein-Hilbert action minimally coupled to scalar fields. Using a Legendre transformation, we formulate the Hamiltonian dynamics in canonically equivalent geometrodynamical and Yang-Mills-type representations, incorporating nontrivial couplings through a geometric structure on the multifield configuration space. Implementing the μ¯-scheme polymerization, we obtain the loop-quantum-corrected Friedmann equations. By focusing on the two-field models as an example, we analyze the effective dynamics for specific potentials. The quantum bouncing, transition, and slow-roll inflationary phases are investigated numerically, and viability of the models is assessed by evaluating the number of e-folds during the inflationary phase for certain given initial conditions. The global behavior of the background evolution is further examined through linear stability and dynamical-systems analyses.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (88)

  1. A. Ashtekar and P. Singh, Loop quantum cosmology: A status report, Classical Quantum Gravity 28, 213001 (2011).
  2. I. Agulló, A. Wang, and E. Wilson-Ewing, Loop quantum cosmology: Relation between theory and observations, in Handbook of Quantum Gravity (Springer, Singapore, 2023).
  3. B. F. Li and P. Singh, Loop quantum cosmology: Physics of singularity resolution and its implications, in Handbook of Quantum Gravity (Springer, Singapore, 2023).
  4. A. Ashtekar, M. Bojowald, and J. Lewandowski, Mathematical structure of loop quantum cosmology, Adv. Theor. Math. Phys. 7, 233 (2003).
  5. M. Bojowald, Loop quantum cosmology, Living Rev. Relativity 8, 11 (2005).
  6. A. Ashtekar, Loop quantum cosmology: An overview, Gen. Relativ. Gravit. 41, 707 (2009).
  7. K. Banerjee, G. Calcagni, and M. Martin-Benito, Introduction to loop quantum cosmology, SIGMA 8, 016 (2012).
  8. A. Ashtekar, Symmetry reduced loop quantum gravity: A bird’s eye view, Int. J. Mod. Phys. D 25, 1642010 (2016).
  9. M. Bojowald, Loop quantum cosmology. I. Kinematics, Classical Quantum Gravity 17, 1489 (2000).
  10. A. Ashtekar, T. Pawlowski, and P. Singh, Quantum nature of the big bang: Improved dynamics, Phys. Rev. D 74, 084003 (2006).
  11. A. Ashtekar, A. Corichi, and P. Singh, Robustness of key features of loop quantum cosmology, Phys. Rev. D 77, 024046 (2008).
  12. M. Bojowald, Absence of singularity in loop quantum cosmology, Phys. Rev. Lett. 86, 5227 (2001).
  13. P. Singh, Are loop quantum cosmos never singular?, Classical Quantum Gravity 26, 125005 (2009).
  14. P. Singh, Loop quantum cosmology and the fate of cosmological singularities, Bull. Astron. Soc. India 42, 121 (2014).
  15. S. Saini and P. Singh, Generic absence of strong singularities and geodesic completeness in modified loop quantum cosmologies, Classical Quantum Gravity 36, 105014 (2019).
  16. A. Ashtekar and E. Wilson-Ewing, Loop quantum cosmology of Bianchi I models, Phys. Rev. D 79, 083535 (2009).
  17. M. Sharma, T. Zhu, and A. Wang, Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology, Commun. Theor. Phys. 71, 1205 (2019).
  18. M. Sharma, G. S. Vicente, L. L. Graef, R. O. Ramos, and A. Wang, Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime, Phys. Rev. D 111, 043501 (2025).
  19. D. W. Chiou, Effective dynamics, big bounces and scaling symmetry in Bianchi type I loop quantum cosmology, Phys. Rev. D 76, 124037 (2007).
  20. M. Martin-Benito, G. A. Mena Marugan, and T. Pawlowski, Loop quantization of vacuum Bianchi I cosmology, Phys. Rev. D 78, 064008 (2008).
  21. A. Ashtekar and E. Wilson-Ewing, Loop quantum cosmology of Bianchi type II models, Phys. Rev. D 80, 123532 (2009).
  22. E. Wilson-Ewing, Loop quantum cosmology of Bianchi type IX models, Phys. Rev. D 82, 043508 (2010).
  23. B. Gupt and P. Singh, Quantum gravitational Kasner transitions in Bianchi-I spacetime, Phys. Rev. D 86, 024034 (2012).
  24. P. Singh and E. Wilson-Ewing, Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology, Classical Quantum Gravity 31, 035010 (2014).
  25. P. Singh, Is classical flat Kasner spacetime flat in quantum gravity?, Int. J. Mod. Phys. D 25, 1642001 (2016).
  26. D. Brizuela, G. A. D. Mena Marugan, and T. Pawlowski, Big bounce and inhomogeneities, Classical Quantum Gravity 27, 052001 (2010).
  27. I. Agullo, J. Olmedo, and V. Sreenath, Observational consequences of Bianchi I spacetimes in loop quantum cosmology, Phys. Rev. D 102, 043523 (2020).
  28. I. Agullo, J. Olmedo, and E. Wilson-Ewing, Observational constraints on anisotropies for bouncing alternatives to inflation, J. Cosmol. Astropart. Phys. 10 (2022) 045.
  29. A. García-Quismondo and G. A. Mena Marugán, The Martin-Benito-Mena Marugan-Olmedo prescription for the Dapor-Liegener model of loop quantum cosmology, Phys. Rev. D 99, 083505 (2019).
  30. A. Garcia-Quismondo and G. A. Mena Marugan, Dapor-Liegener formalism of loop quantum cosmology for Bianchi I spacetimes, Phys. Rev. D 101, 023520 (2020).
  31. W. C. Gan, L. L. Graef, R. O. Ramos, G. S. Vicente, and A. Wang, Quantum damping of cosmological shear: A new prediction from loop quantum cosmologies, Phys. Rev. Lett. 136, 251501 (2026).
  32. A. Ashtekar and D. Sloan, Probability of inflation in loop quantum cosmology, Gen. Relativ. Gravit. 43, 3619 (2011).
  33. B. F. Li, P. Singh, and A. Wang, Genericness of pre-inflationary dynamics and probability of the desired slow-roll inflation in modified loop quantum cosmologies, Phys. Rev. D 100, 063513 (2019).
  34. L. Linsefors and A. Barrau, Duration of inflation and conditions at the bounce as a prediction of effective isotropic loop quantum cosmology, Phys. Rev. D 87, 123509 (2013).
  35. L. N. Barboza, L. L. Graef, and R. O. Ramos, Warm bounce in loop quantum cosmology and the prediction for the duration of inflation, Phys. Rev. D 102, 103521 (2020).
  36. L. N. Barboza, G. L. L. W. Levy, L. L. Graef, and R. O. Ramos, Constraining the Barbero-Immirzi parameter from the duration of inflation in loop quantum cosmology, Phys. Rev. D 106, 103535 (2022).
  37. A. Corichi and A. Karami, On the measure problem in slow roll inflation and loop quantum cosmology, Phys. Rev. D 83, 104006 (2011).
  38. M. Sharma, M. Shahalam, Q. Wu, and A. Wang, Preinflationary dynamics in loop quantum cosmology: Monodromy Potential, J. Cosmol. Astropart. Phys. 11 (2018) 003.
  39. J. Mielczarek, Possible observational effects of loop quantum cosmology, Phys. Rev. D 81, 063503 (2010).
  40. L. L. Graef and R. O. Ramos, Probability of warm inflation in loop quantum cosmology, Phys. Rev. D 98, 023531 (2018).
  41. M. Benetti, L. Graef, and R. O. Ramos, Observational constraints on warm inflation in loop quantum cosmology, J. Cosmol. Astropart. Phys. 10 (2019) 066.
  42. G. L. L. W. Levy and R. O. Ramos, α-attractor potentials in loop quantum cosmology, Phys. Rev. D 110, 043507 (2024).
  43. E. Ranken and P. Singh, Non-singular power-law and assisted inflation in loop quantum cosmology, Phys. Rev. D 85, 104002 (2012).
  44. A. Paliathanasis and G. Leon, Hyperbolic inflationary model with nonzero curvature, Phys. Lett. B 834, 137407 (2022).
  45. C. B. Chen and J. Soda, Geometric structure of multi-form-field isotropic inflation and primordial fluctuations, J. Cosmol. Astropart. Phys. 05 (2022) 029.
  46. M. De Angelis and C. van de Bruck, Adiabatic and isocurvature perturbations in extended theories with kinetic couplings, J. Cosmol. Astropart. Phys. 10 (2023) 023.
  47. S. Mizuno and S. Mukohyama, Primordial perturbations from inflation with a hyperbolic field-space, Phys. Rev. D 96, 103533 (2017).
  48. A. R. Brown, Hyperbolic inflation, Phys. Rev. Lett. 121, 251601 (2018).
  49. D. H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rep. 314, 1 (1999).
  50. A. D. Linde, Hybrid inflation, Phys. Rev. D 49, 748 (1994).
  51. R. O. Ramos, Fine tuning solution for hybrid inflation in dissipative chaotic dynamics, Phys. Rev. D 64, 123510 (2001).
  52. A. D. Linde and A. Riotto, Hybrid inflation in supergravity, Phys. Rev. D 56, R1841 (1997).
  53. T. Cailleteau, L. Linsefors, and A. Barrau, Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology, Classical Quantum Gravity 31, 125011 (2014).
  54. J. Grain, A. Barrau, and A. Gorecki, Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation, Phys. Rev. D 79, 084015 (2009).
  55. D. W. Chiou and K. Liu, Cosmological inflation driven by holonomy corrections of loop quantum cosmology, Phys. Rev. D 81, 063526 (2010).
  56. E. Wilson-Ewing, Holonomy corrections in the effective equations for scalar mode perturbations in loop quantum cosmology, Classical Quantum Gravity 29, 085005 (2012).
  57. A. Corichi and A. Karami, Loop quantum cosmology of k=1 FLRW: Effects of inverse volume corrections, Classical Quantum Gravity 31, 035008 (2014).
  58. L. Iacconi and D. J. Mulryne, Multi-field inflation with large scalar fluctuations: Non-Gaussianity and perturbativity, J. Cosmol. Astropart. Phys. 09 (2023) 033.
  59. D. Nandi and S. Shankaranarayanan, Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field, J. Cosmol. Astropart. Phys. 10 (2016) 008.
  60. X. Zhang, Loop quantum cosmology, modified gravity and extra dimensions, Universe 2, 15 (2016).
  61. A. Corichi and P. Singh, Is loop quantization in cosmology unique?, Phys. Rev. D 78, 024034 (2008).
  62. K. A. Meissner, Black hole entropy in loop quantum gravity, Classical Quantum Gravity 21, 5245 (2004).
  63. R. P. Vyas and M. J. Joshi, The Barbero–Immirzi parameter: An enigmatic parameter of loop quantum gravity, Physics 4, 1094 (2022).
  64. A. Ashtekar, T. Pawlowski, and P. Singh, Quantum nature of the big bang: An analytical and numerical investigation. I., Phys. Rev. D 73, 124038 (2006).
  65. G. Barca, E. Giovannetti, and G. Montani, An overview on the nature of the bounce in LQC and PQM, Universe 7, 327 (2021).
  66. W. C. Gan, X. M. Kuang, Z. H. Yang, Y. Gong, A. Wang, and B. Wang, Nonexistence of quantum black and white hole horizons in an improved dynamic approach, Sci. China Phys. Mech. Astron. 67, 280411 (2024).
  67. A. Ashtekar, T. Pawlowski, and P. Singh, Quantum nature of the big bang, Phys. Rev. Lett. 96, 141301 (2006).
  68. A. Ashtekar and D. Sloan, Loop quantum cosmology and slow roll inflation, Phys. Lett. B 694, 108 (2011).
  69. P. Singh, K. Vandersloot, and G. V. Vereshchagin, Non-singular bouncing universes in loop quantum cosmology, Phys. Rev. D 74, 043510 (2006).
  70. X. Zhang and Y. Ling, Inflationary universe in loop quantum cosmology, J. Cosmol. Astropart. Phys. 08 (2007) 012.
  71. T. Zhu, A. Wang, K. Kirsten, G. Cleaver, and Q. Sheng, Universal features of quantum bounce in loop quantum cosmology, Phys. Lett. B 773, 196 (2017).
  72. T. Zhu, A. Wang, G. Cleaver, K. Kirsten, and Q. Sheng, Pre-inflationary universe in loop quantum cosmology, Phys. Rev. D 96, 083520 (2017).
  73. J. Saeed, R. Pan, C. Brown, G. Cleaver, G. Clevear, and A. Wang, Universal properties of the evolution of the universe in modified loop quantum cosmology, Universe 10, 397 (2024).
  74. B. F. Li, P. Singh, and A. Wang, Phenomenological implications of modified loop cosmologies: An overview, Front. Astron. Space Sci. 8, 701417 (2021).
  75. B. F. Li, P. Singh, and A. Wang, Qualitative dynamics and inflationary attractors in loop cosmology, Phys. Rev. D 98, 066016 (2018).
  76. A. Bhardwaj, E. J. Copeland, and J. Louko, Inflation in loop quantum cosmology, Phys. Rev. D 99, 063520 (2019).
  77. D. Baumann, Inflation, Physics of the Large and the Small (World Scientific, Singapore, 2011).
  78. A. Berera, H. Bernardo, S. Brahma, J. Calderón-Figueroa, R. O. Ramos, and M. W. Toomey, Heterotic warm inflation, J. High Energy Phys. 06 (2026) 099.
  79. C. van de Bruck and M. Robinson, Power spectra beyond the slow roll approximation in theories with non-canonical kinetic terms, J. Cosmol. Astropart. Phys. 08 (2014) 024.
  80. E. J. Copeland, A. R. Liddle, D. H. Lyth, E. D. Stewart, and D. Wands, False vacuum inflation with Einstein gravity, Phys. Rev. D 49, 6410 (1994).
  81. M. Cicoli, G. Dibitetto, and F. G. Pedro, Out of the swampland with multifield quintessence?, J. High Energy Phys. 10 (2020) 035.
  82. D. Samart and B. Gumjudpai, Phantom field dynamics in loop quantum cosmology, Phys. Rev. D 76, 043514 (2007).
  83. S. Das, S. Hussain, D. Nandi, R. O. Ramos, and R. Silva, Stability analysis of warm quintessential dark energy model, Phys. Rev. D 108, 083517 (2023).
  84. N. Dimakis, A. Paliathanasis, P. A. Terzis, and T. Christodoulakis, Cosmological solutions in multiscalar field theory, Eur. Phys. J. C 79, 618 (2019).
  85. M. Shahalam, M. Sharma, Q. Wu, and A. Wang, Preinflationary dynamics in loop quantum cosmology: Power-law potentials, Phys. Rev. D 96, 123533 (2017).
  86. C. G. Boehmer and N. Chan, Dynamical systems in cosmology, in Dynamical and Complex Systems (World Scientific, Singapore, 2017), pp. 121–156.
  87. M. Lakshmanan and S. Rajasekar, Nonlinear Dynamics: Integrability, Chaos, and Patterns (Springer, New York, 2003), ISBN [Amazon][WorldCat].
  88. M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Anomaly freedom in perturbative loop quantum gravity, Phys. Rev. D 78, 063547 (2008).

Outline

Information

Phys. Rev. D 114, 043503– Published 4 August, 2026
  • Received 1 April 2026
  • Accepted 23 June 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation